This article provides a short history and detailed theoretical overview of the gas centrifuge in the United States, from 1934 to 1985. Organized into two major sections, the article begins with a history of centrifuge development, including Jesse Beams' work at the University of Virginia, the Manhattan Project's consideration and abandonment of the centrifuge as a means of enriching uranium for the first atomic bombs, post-World War II research activity to improve the technology, and the cancellation of the entire centrifuge effort in 1985. The longer, second section details the theoretical contributions of U.S. scientists in estimating the performance of the machines and in understanding the internal gas flows in order to improve centrifuge design and performance. The article contains mathematical explanations of the processes involved as well as supporting appendices.